The Boat from Europe in 1906

I'm trying to dig for my roots in eastern Europe.My grandfather came over in the early 1900s through Ellis Island.The family story is that when he arrived, he was told to change his name to Abramson.Prior to that we believe that his name was Sippovich or something spelled similarly.He originated from Western Russia along with many others.Does anyone else have a similar story of ancestors being told to change their names completely when they immigrated?Thanks.